Higher-Order Derivatives

AP Calculus · Axiom Academy

LESSON Higher-Order Derivatives Finding derivatives of derivatives Step 1: What are Higher-Order Derivatives? You find higher-order derivatives by differentiating repeatedly. The second derivative measures how fast the slope is changing—this is acceleration in physics! There are several ways to write derivatives: The Lagrange notation is most common. The number of primes indicates the order of the derivative. Find the first, second, and third derivatives of : Physics: If s(t) is position, then s'(t) is velocity and s''(t) is acceleration. Calculus: The second derivative test identifies local maxima and minima. Concavity is determined by the second derivative. You've mastered higher-order derivatives! Next: Logarithmic differentiation for complex products and quotients.

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